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A fake knot (i.e., a knot equivalent to the unknot) created by tying a square knot, then looping one end twice through the knot such that when both ends are pulled, the knot ...

The trefoil knot 3_1, also called the threefoil knot or overhand knot, is the unique prime knot with three crossings. It is a (3, 2)-torus knot and has braid word sigma_1^3. ...

A knot K is an n-embeddable knot if it can be placed on a genus n standard embedded surface without crossings, but K cannot be placed on any standardly embedded surface of ...

A chiral knot is a knot which is not capable of being continuously deformed into its own mirror image. A knot that can be so deformed is then called an amphichiral knot. ...

A hyperbolic knot is a knot that has a complement that can be given a metric of constant curvature -1. All hyperbolic knots are prime knots (Hoste et al. 1998). A prime knot ...

The figure eight knot, also known as the Flemish knot and savoy knot, is the unique prime knot of four crossings 04-001. It has braid word ...

A knot equivalent to a polygonal knot. Knots which are not tame are called wild knots.

An amphichiral knot is a knot that is capable of being continuously deformed into its own mirror image. More formally, a knot K is amphichiral (also called achiral or ...

A knot K in S^3=partialD^4 is a slice knot if it bounds a disk Delta^2 in D^4 which has a tubular neighborhood Delta^2×D^2 whose intersection with S^3 is a tubular ...

A knot diagram in which none of the crossings are reducible.